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Data Mining By IK Unit 4

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Unit 4

Data mining can be classified into two categories

1) Descriptive mining: describes concepts or task-relevant data sets in concise, summarative, informative, discriminative forms

2) Predictive mining: Based on data and analysis, constructs models for the database, and predicts the trend and properties of unknown data

CONCEPT DESCRIPTION:

Characterization: Provides a brief and clear summarization of the given collection of data.

Comparison: Provides descriptions comparing two or more collections of data.

Difference between Concept Descriptions and OLAP

Functionality Concept description OLAP Complex data types and aggregation

Concept Description can handle complex data types including numeric ,non numeric, spatial, text and can apply aggregation on them if necessary.

restricted to a small number of dimension and measure types. Many dimensions confine to non numeric data. And count (), Sum (), average () can only be applied to numeric data.

User-control versus automation

It is generally automated process

OLAP is user-controlled process. S;/ince user has to decide when to roll up, when to drill down etc..

Data

Mining

Descriptive Predictive


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DATA GENERALIZATION AND SUMMARIZATION BASED

CHARACTERIZATION Data generalization: It is a process which abstracts a large set of task-relevant data in a database from low conceptual levels to higher ones. For example the sales according to locations can be generalized as below.

There are mainly two approaches for data generalization:

1) Data cube approach (OLAP approach) 2) Attribute-oriented induction approach

ATTRIBUTE ORIENTED INDUCTION:

The attribute-oriented induction (AOI) approach to concept description was first proposed in 1989.The general idea behind attribute oriented induction is as follows. STEP1: DATA FOCUSING:

Collect the task-relevant data by using data mining query on huge set of data. Selecting the relevant set of data not only makes mining more efficient, but also derives more meaningful results than mining the entire database.

For Example: use Big University DB mine characteristics as “Science Students” in relevance to name, gender, major, birth place, birth date, residence, phone gpa from student where status in “graduate” The above query collect task relevant data .i.e data related to graduate students which results in following table.

Continent

country

state

district

city

street

Name Gen der

Major Birth-Place Birth_date Residence Phone # GPA

Jim Woodman M CS Vancouver,BC ,Canada

8-12-76 3511 Main St., Richmond

687-4598 3.67

Scott Lachance M CS Montreal, Que, Canada

28-7-75 345 1st Ave., Richmond

253-9106 3.70

Laura Lee …

F …

Physics …

Seattle, WA, USA …

25-8-70 …

125 Austin Ave., Burnaby …

420-5232 …

3.83 …


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STEP 2: DATA GENERALIZATION: Depending on situation data generalization is performed by using following methods.

1. Attribute removal: An attribute is removed if there is a large set of distinct values for that attribute but (1) There is no generalization operator on it, or (2) Attribute’s higher level concepts are expressed in terms of other attributes. For Example attribute NAME can be removed from the table because it has a large set of distinct values. And an attribute CITY can be removed if it is already expressed in LOCATION attribute. 2. Attribute generalization: If there is a large set of distinct values for an attribute in the initial working relation, and there exists a set of generalization operators on the attribute, then a generalization operator should be selected and applied to the attribute. . For Example consider attribute marks of students (which is a continuous valued attribute) which can be generalized in terms of grades. Some terms under attribute generalization:-

Attribute generalization control: The process of controlling the level of generalization for an attribute is known as attribute generalization control. Attribute generalization threshold control: Setting one generalization threshold for all of the attributes, or sets one threshold for each attribute. Generalized relation threshold control: unlike setting threshold for an attribute, Generalized threshold control sets a threshold for the generalized relation.

Attribute Name

Action Reason

Name Remove Large Domain and cannot be generalized Gender Nothing Very small domain Major Generalized Generalized to arts, science, Engineering, business Birth_place Generalized

(Removed and replaced with another attribute)

If generalized operator exists then generalize to country level and replace birth_place with Birth Country ( should no cross the generalized relation threshold)

Birth_date --do-- Birth_date (30-05-1987) > age(25) > age range(25…30) Residence ---do-- Number > street > residence city > state > country Phone Removed Large Domain and cannot be generalized GPA Generalized {3.75 – 4.0 ,3.5 – 3.75 ….} > { Excellent , Very good…}


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STEP 3: DATA AGGREGATION It is done by merging identical, generalized tuples and accumulating their respective counts.

STEP 4: PRESENTATION OF THE GENERALIZED RELATION Generalized relation (table)

a) CROSS-TABULATION Descriptions can also be visualized in the form of cross-tabulations, or crosstabs. In a two-dimensional crosstab, each row represents a value from an attribute, and each column represents a value from another attribute.

b) BAR CHART AND PIE CHART The sales data of the crosstab shown in above table can be transformed into the bar chart as well as pie chart.

Gender Major Birth_Country Age_range Residence_city GPA Count

M Science Canada 20-25 Richmond Very-good 16

F Science Foreign 25-30 Burnaby Excellent 22

… … … … … … …


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c) REPRESENTATION IN TERM OF LOGICAL RULES: Generalized relation may also be represented in the form of logic rules. These rules are also known as quantitative rule (since they represent some quantity). When a quantitative rule represents some generalized information regarding target class of data then it is known as quantitative characteristic rule. T-weight is an interestingness measure that describes the typicality of each disjunct in the rule. The t-weight is represented as

And the quantitative characteristic rule should be expressed in the form

Example of Quantitative characteristic rule:

Here t:25.00% is number of computers sold in Asia (1000) / total computer sold (4000)


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Algorithm: Attribute oriented induction. Mining gen eralized characteristics in a relational database given a user’s data mining request. Input:

DB, a relational database; DMQuery, a data mining query; a list, a list of attributes (containing attributes, ai); Gen(ai), a set of concept hierarchies or generalization operators on attributes, ai; a gen thresh(ai), attribute generalization thresholds for each ai.

Output: P, a Prime generalized relation. Method: 1. W get task relevant data (DMQuery, DB); // Let W, the working relation, hold the task-relevant data. 2. Prepare for generalization (W); // This is implemented as follows.

(a) Scan W and collect the distinct values for each attribute, ai. (Note: If W is very large, this may be done by examining a sample of W.)

(b) For each attribute ai, determine whether ai should be removed, and if not, compute its minimum desired level Li based on its given or default attribute threshold, and determine the mapping pairs (v, v’), where v is a distinct value of ai in W, and v’ is its corresponding generalized value at level Li.

3. P generalization (W), The Prime generalized relation, P, is derived by replacing each value v in W by its corresponding v’ in the mapping while accumulating count and computing any other aggregate values. This step can be implemented efficiently using either of the two following variations:

(a) For each generalized tuple, insert the tuple into a sorted prime relation P by a binary search: if the tuple is already in P, simply increase its count and other aggregate values accordingly; otherwise, insert it into P.

(b) Since in most cases the number of distinct values at the prime relation level is small, the prime relation can be coded as an m-dimensional array where m is the number of attributes in P, and each dimension contains the corresponding generalized attribute values. Each array element holds the corresponding count and other aggregation values, if any. The insertion of a generalized tuple is performed by measure aggregation in the corresponding array element.


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ANALYTICAL CHARACTERIZATION: ANALYSIS OF ATTRIBUTE RELEVANCE

Why perform attribute relevance analysis? It is very important to know which attribute is relevant for analysis and which attribute is not. Methods should be introduced to perform attribute (or dimension )relevance Analysis in order to filter out statistically irrelevant or weakly relevant attributes, and retain or even rank the most relevant attributes for the descriptive mining task at hand. Class characterization that includes the analysis of attribute/dimension relevance is called analytical characterization. Class comparison that includes such analysis is called analytical comparison. An attribute or dimension is considered highly relevant with respect to a given class if it is likely that the values of the attribute or dimension may be used to distinguish the class from others. Methods for attribute relevance

1) Information gain (ID3) 2) Gain ratio (C4.5) 3) Gini index 4) Contingency table statistics 5) Uncertainty coefficient

Information gain (ID3) is mainly used method for attribute relevance analysis. It is done as follows STEP 1. DATA COLLECTION Collect data for both the target class(graduate students) and the contrasting class(under graduate) by query processing. The target class is the class to be characterized, whereas the contrasting class is the set of comparable data that are not in the target class. Fig: Target class data


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Fig: contrasting class data

STEP 2: PRELIMINARY RELEVANCE ANALYSIS BY APPLYING CONSERVATIVE AOI In this step preliminary analysis is done by attribute oriented induction and unnecessary attribute such as name, phone no. are removed. Attributes are also generalized by keeping low generalization threshold value.

Total graduate students:120

Total undergraduate students 130

STEP 3: REMOVE IRRELEVANT OR WEEKLY RELEVANT ATTRIBUTES USING THE RELEVANCE MEASURE. Here we are using information gain as the relevant measure, which is performed as follows. 1) Calculate expected information required to classify an arbitrary tuple is given by

Where’ S’ is total number of samples si are the samples of class ‘ci’. By substituting the values we get.

2) Calculate entropy of each attribute: e.g. major


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By substituting the values.

3) Information gain obtained by partitioning on attribute A

By substituting the values:

In the similar manner the information gain of rest of the attributes are

Gain (gender) = 0.0003 Gain (birth_country) = 0.0407 Gain (major) = 0.2115 Gain (gpa) = 0.4490

Gain (age_range) = 0.5971 Now, remove irrelevant/weakly relevant attributes from candidate which do not satisfy the threshold value 0.1 drop gender, birth_country and remove contrasting class candidate relation. This data is known as initial target class working relation. This is shown below.

STEP 4: GENERATE THE CONCEPT DESCRIPTION USING ATTRIBUTE ORIENTED INDUCTION. Perform AOI using less conservative set of AOI threshold.


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MINING CLASS COMPARISONS: DISCRIMINATING BETWEEN

DIFFERENT CLASSES Class discrimination or comparison (hereafter referred to as class comparison) mines descriptions that distinguish a target class from its contrasting classes. Notice that the target and contrasting classes must be comparable in the sense that they share similar dimensions and attributes. For example, the three classes, person, address, and item, are not comparable. Attribute generalization process described for class characterization can be modified so that the generalization is performed synchronously among all the classes compared. This allows the attributes in all of the classes to be generalized to the same levels of abstraction.

1. DATA COLLECTION: The set of relevant data in the database is collected by query processing and is partitioned respectively into a target class and one or a set of contrasting class(es). use Big_University_DB mine comparison as “grad_vs_undergrad_students” in relevance to name, gender, major, birth_place, birth_date, residence, phone#, gpa for “graduate_students” where status in “graduate” versus “undergraduate_students” where status in “undergraduate” analyze count% from student Initial target class

Initial Contrasting Class

2. DIMENSION RELEVANCE ANALYSIS: If there are many dimensions, then dimension relevance analysis should be performed on these classes to select only the highly relevant dimensions for further analysis. Correlation or entropy-based measures can be used for this step. Irrelevant or weakly relevant dimensions, such as name, gender, birth place, residence, and phone#, are removed from the resulting classes. Only the highly relevant attributes are included in the subsequent analysis.


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3. SYNCHRONOUS GENERALIZATION: Generalization is performed on the target

class to the level controlled by a user- or expert-specified dimension threshold, which results in a prime target class relation. The concepts in the contrasting class (es) are generalized to the same level as those in the prime target class relation, forming the prime contrasting class(es) relation.

4. Presentation of the derived comparison: The resulting class comparison description can be visualized in the form of tables, graphs, and rules. This presentation usually includes a “contrasting” measure such as count% (percentage count) that reflects the comparison between the target and contrasting classes. The user can adjust the comparison description by applying drill-down, roll-up, and other OLAP operations to the target and contrasting classes, as desired.

A quantitative discriminant rule for the target class of a given comparison description is written in the form.

The d-weight for qa is the ratio of the number of tuples from the initial target class working relation that are covered by qa to the total number of tuples in both the initial target class and contrasting class working relations that are covered by qa. Formally, the d-weight of qa for the class Cj is defined as,

For Example,

Note: d-weight=Graduate (90) / (Graduate (90) +undergraduate (210))


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CLASS DESCRIPTION: PRESENTATION OF BOTH CHARACTERIZATION AND COMPARISON

QUANTITATIVE DESCRIPTION RULE: A quantitative characteristic rule and a quantitative discriminant rule for the same class can be combined to form a quantitative description rule for the class, which displays the t-weights and d-weights associated with the corresponding characteristic and discriminant rules. The quantitative description rule is expressed in te form,

The above table can be expressed in with T-weight and D-weight as follows,

The quantitative description rule for the target class, Europe, is

Note: t-weight of TV in Europe = (sales of tv in Europe)/(sales of tv in europe+sales of computer in europe) d-weight of TV in Europe = ( sales of tv in Europe)/(sales of tv in Europe +Sales of TV in north America) PLEASE WRITE T-WEIGTH AND D-WEIGHT FORMULA WITH THIS CONTENT.


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MINING DESCRIPTIVE STATISTICAL MEASURES IN LARGE

DATABASES Relational database systems provide built-in aggregate functions: count(), sum(), avg(), max(), and min(). But, for doing data mining we need more functions to describe the central tendency and dispersion of data. Measures of central tendency include mean, median, mode, and midrange, while measures of data dispersion include quartiles, outliers, variance, and other statistical measures. MEASURING THE CENTRAL TENDENCY The most common and most effective numerical measure of the “center" of a set of data is the (arithmetic) mean. Let x1, x2…… xn be a set of n values or observations. The mean of this set of values is

Sometimes, each value xi in a set may be associated with a weight wi, for i = 1…n. The weights reflect the significance, importance, or occurrence frequency attached to their respective values. In this case, we can compute the weighted arithmetic mean as,

For skewed data, a better measure of center of data is the median, M. Suppose that the values forming a given set of data are in numerical order. The median is the middle value of the ordered set if the number of values n is an odd number; otherwise (i.e.if n is even), it is the average of the middle two values. For example, for grouped data, the median, obtained by interpolation, is given by

The mode for a set of data is the value that occurs most frequently in the set. Data sets with one, two, or three modes are respectively called unimodal, bimodal, and trimodal. If a data set has more than three modes, it is multimodal. For unimodal frequency curves that are moderately skewed (asymmetrical), we have the following empirical relation

The midrange, that is, the average of the largest and smallest values in a data set, can be used to measure the central tendency of the set of data.


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MEASURING THE DISPERSION OF DATA The most common measures of data dispersion are the five-number summary (based on quartiles), the interquartile range, and standard deviation. The plotting of boxplots (which show outlier values) also serves as a useful graphical method. The first quartile, denoted by Q1, is the 25-th percentile; and the third quartile, denoted by Q3, is the 75-th percentile. INTERQUARTILE RANGE: The distance between the first and third quartiles is a simple measure of spread that gives the range covered by the middle half of the data. This distance is called the interquartile range (IQR), and is defined as,

One common rule of thumb for identifying suspected outliers is to single out values falling at least 1.5 * IQR above the third quartile or below the first quartile. The five number summary of a distribution consists of the median M, the quartiles Q1 and Q3, and the smallest and largest individual observations, written in the order

Minimum, Q1, M, Q3, Maximum A popularly used visual representation of a distribution is the boxplot. In a boxplot: 1. The ends of the box are at the quartiles, so that the box length is the interquartile range, IQR. 2. The median is marked by a line within the box. 3. Two lines (called whiskers) outside the box extend to the smallest (Minimum) and largest (Maximum) observations. Figure

VARIANCE AND STANDARD DEVIATION The variance of n observations x1, x2…. xn is

Standard deviation: the square root of the variance

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